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3. * Let X1,,Xn be a random sample from the distribution with p.d.f. f(x)={e(x),0,x>otherwise where the value of is unknown. (i) * Show that Xn is a biased estimator of . [2 marks] (ii)* Derive an expression for bias (Xn) and discuss what happens to its value as n. [2 marks] (iii)* Can you propose an alternative, unbiased estimator of ?[1mark].

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3. * Let X1,,Xn be a random sample from the distribution with p.d.f. f(x)={e(x),0,x>otherwise where the value of is unknown. (i) * Show that Xn is a biased estimator of . [2 marks] (ii)* Derive an expression for bias (Xn) and discuss what happens to its value as n. [2 marks] (iii)* Can you propose an alternative, unbiased estimator of ?[1mark]

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  • 1. 3. * Let X1,,Xn be a random sample from the distribution with p.d.f. f(x)={e(x),0,x>otherwise where the value of is unknown. (i) * Show that Xn is a biased estimator of . [2 marks] (ii)* Derive an expression for bias (Xn) and discuss what happens to its value as n. [2 marks] (iii)* Can you propose an alternative, unbiased estimator of ?[1mark]